Statistics Homework Solutions 155

# Statistics Homework Solutions 155 - 155 SECTION 6.10 1000...

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SECTION 6.10 155 (b) The total number of observation is n 1000. The expected values are np 1 , np 2 and np 3 , or 900, 50, and 50. (c) The observed values are 860, 60, and 80. χ 2 860 900 2 900 60 50 2 50 80 50 2 50 21 7778. (d) There are 3 1 2 degrees of freedom. From the χ 2 table, P 0 005. A computer package gives P 1 9 10 5 . The true percentages differ from 90%, 5%, and 5%. 3. The row totals are O 1 173 and O 2 210. The column totals are O 1 181, O 2 99, O 3 31, O 4 11, O 5 61. The grand total is O 383. The expected values are E ij O i O j O , as shown in the following table. Net Excess Capacity 0% 0 – 10% 11 – 20% 21 – 30% 30% Small 81.7572 44.7180 14.0026 4.9687 27.5535 Large 99.2428 54.2820 16.9974 6.0313 33.4465 There are 2 1 5 1 4 degrees of freedom. χ 2 2 i 1 5 j 1 O ij E ij 2 E ij 12 945. From the χ 2 table, 0 01 P 0 05. A computer package gives P 0 012. It is reasonable to conclude that the distributions differ. 5. The row totals are
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